Depletion optimization and photon efficiency in laser isotope separation of deuterium

J. C. Vanderleeden

doi:10.1364/AO.17.000785

Applied Optics
Vol. 17,
Issue 5,
pp. 785-796
(1978)
•https://doi.org/10.1364/AO.17.000785

Depletion optimization and photon efficiency in laser isotope separation of deuterium

J. C. Vanderleeden

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
J. C. Vanderleeden, "Depletion optimization and photon efficiency in laser isotope separation of deuterium," Appl. Opt. 17, 785-796 (1978)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

The depletion optimization of one of the isotopic components in a gas stream is considered, using a one-photon laser separation process, when the absorption path is in the kilometer range. A multiple-pass cylindrical geometry is proposed with the gas flowing through a tube enclosed by aspherical mirrors. Radiation is injected such that adjustment of the mirror parameters establishes a flux distribution which optimizes the depletion while it minimizes losses from incomplete absorption. The mirror parameters are derived and application to deuterium separation is discussed. This approach is also useful in optical amplifiers and resonators to maximize energy extraction.

Full Article | PDF Article

More Like This

Laser isotope separation of rare earth elements

N. V. Karlov, B. B. Krynetskii, V. A. Mishin, and A. M. Prokhorov
Appl. Opt. 17(6) 856-862 (1978)

Laser Isotope Separation Using Two-Photon Selective Excitation; Its Quantum Efficiency and Separation Factor

Yung S. Liu
Appl. Opt. 13(11) 2505-2511 (1974)

Coherence of a light beam through an optically dense turbid layer

D. A. de Wolf
Appl. Opt. 17(8) 1280-1285 (1978)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (6)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (3)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (60)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Parameter	Value	Type
D_max, isotopic depletion	50%	Assumed
d, reaction chamber length	75 m	Assumed
$λ (d) = σ \int_{0}^{d} N (z) d z$	0.15	Assumed
σ, absorption cross section	3.32 × 10⁻²⁰ cm² (∼201/mole-cm)	Exp. known
P_D, partial pressure of HDCO	3.42 Pa	Calculated, at 300 K
Redeuteration ratio H₂CO/ HDCO	4170	Exp. known
P_H, partial pressure of H₂CO	14.3 kPa (≈100Torr)	Calculated, at 300 K
Th, formaldehyde throughput	4.59 m³/sec (≈26.5 mole/sec)	Calculated, at 300 K and 0.142 atm
Fraction of photons lost	<15%	Assumed
m, number of passes through reaction chamber	14	Calculated
α₁, apex angle	6.67 × 10⁻³ rad	Assumed
R_#1, radius of mirror 1	0.923 m	Calculated
R_#2, radius of mirror 2	1.08 m	Calculated
R_rc, radius of RC	1.12 m	Calculated
A_w, area of entrance window	1.26 m²	Calculated
V, vapor velocity	1.16 m/sec	Calculated
N_R, Reynolds number	≈44,400 (turbulent flow)	Calculated
Fⁱ incident laser flux density	1.44 × 10²¹/m² sec	Calculated
∊, photon energy	≈3.54 eV	Exp. known
P_laser, average laser output	1.03 kW	Calculated
θ, laser beam divergence	<0.16 mR	See Sec. V.A
δν, laser linewidth	≈0.1 cm⁻¹	Exp. known
C_e, laser energy cost	≈11 $/kg D₂O	Calculated

Condition	Origin/type	Comment
(1) Zero laser beam divergence	Optical/restriction	Relaxation of restriction results in smearing out of flux distribution. Slightly lower depletion, as long as V(r) constant or only slowly changing
(2) Neglect turbulence in feed gas	Optical, hydrodynamic/approximation	Turbulence causes beam wander and decreases depletion. Approximation valid if α₁ ≲ 3mσ(α).
(3) Isotopic depletion is independent of pulsed or cw laser operation	Optical, molecular, hydrodynamic/approximation	Valid provided (1) averaged pulsed output equals cw output, (2) nonlinear effects can be neglected, (3) V(r)/f ≳ d, where f is repetition rate.
(4) Separation process involves absorption of a single photon	Molecular/restriction	Basic consideration. RC design not useful in two-photon or multiphoton processes unless F(r,z) saturates lower transitions
(5) Isotopic selectivity is infinite	Molecular/assumption	Simplifies rate equation analysis but does not affect RC design concept.
(6) Time-averaged gas velocity V(r) is parallel to z axis and not z dependent	Hydrodynamic/assumption	Valid in laminar and turbulent flow for small pressure drop over RC length. Design concept still valid if V(r) also z dependent.
(7) Diffusion-related mass transfer ≪ mass transfer due to V(r)	Hydrodynamic/approximation	Basic to RC design consideration. Depletion is increasingly independent of F(r,z) distribution with increasing violation of inequality [see Sec. III.A, Eq. (7)]
(8) Gaussian optics	Optical/approximation	Good approximation for present small values of apex angle α₁.
(9) F(r,z) distribution satisfies condition for maximum depletion $\int {}_{0}^{d}F (r, z) d z \propto V (r)$	Optical/approximation	Requires approximations of Eqs. (3), (12), and (14). Typically valid to better than 10%. Depletion is not sensitive to small deviations from optimum F(r,z) if V(r) constant or slowly changing.

Characteristic	Reaction chamber designs

	Present work	Stable resonator^a	Hill and Hartley9	Welsh et al.10
Mirror type	Aspherical/convex-concave	Spherical/concave-concave	Ellipsoidal/concave-concave	Spherical/concave-split concave
Optimum flux distribution^b	Yes	No	No	No
Radiation coupling into RC	Around one mirror	Around one mirror	Around one mirror	Through slot or hole at center of one mirror
Coupling of multiple beams into RC	Possible	Possible	Possible	Not possible
Optical isolation of laser from un-absorbed power in RC	Achieved with polarizer	Achieved with polarizer	Not necessary	Not necessary
Estimated ranking in order of increasing cost	4	1	3	z

Parameter	Value	Type
D_max, isotopic depletion	50%	Assumed
d, reaction chamber length	75 m	Assumed
$λ (d) = σ \int_{0}^{d} N (z) d z$	0.15	Assumed
σ, absorption cross section	3.32 × 10⁻²⁰ cm² (∼201/mole-cm)	Exp. known
P_D, partial pressure of HDCO	3.42 Pa	Calculated, at 300 K
Redeuteration ratio H₂CO/ HDCO	4170	Exp. known
P_H, partial pressure of H₂CO	14.3 kPa (≈100Torr)	Calculated, at 300 K
Th, formaldehyde throughput	4.59 m³/sec (≈26.5 mole/sec)	Calculated, at 300 K and 0.142 atm
Fraction of photons lost	<15%	Assumed
m, number of passes through reaction chamber	14	Calculated
α₁, apex angle	6.67 × 10⁻³ rad	Assumed
R_#1, radius of mirror 1	0.923 m	Calculated
R_#2, radius of mirror 2	1.08 m	Calculated
R_rc, radius of RC	1.12 m	Calculated
A_w, area of entrance window	1.26 m²	Calculated
V, vapor velocity	1.16 m/sec	Calculated
N_R, Reynolds number	≈44,400 (turbulent flow)	Calculated
Fⁱ incident laser flux density	1.44 × 10²¹/m² sec	Calculated
∊, photon energy	≈3.54 eV	Exp. known
P_laser, average laser output	1.03 kW	Calculated
θ, laser beam divergence	<0.16 mR	See Sec. V.A
δν, laser linewidth	≈0.1 cm⁻¹	Exp. known
C_e, laser energy cost	≈11 $/kg D₂O	Calculated

Condition	Origin/type	Comment
(1) Zero laser beam divergence	Optical/restriction	Relaxation of restriction results in smearing out of flux distribution. Slightly lower depletion, as long as V(r) constant or only slowly changing
(2) Neglect turbulence in feed gas	Optical, hydrodynamic/approximation	Turbulence causes beam wander and decreases depletion. Approximation valid if α₁ ≲ 3mσ(α).
(3) Isotopic depletion is independent of pulsed or cw laser operation	Optical, molecular, hydrodynamic/approximation	Valid provided (1) averaged pulsed output equals cw output, (2) nonlinear effects can be neglected, (3) V(r)/f ≳ d, where f is repetition rate.
(4) Separation process involves absorption of a single photon	Molecular/restriction	Basic consideration. RC design not useful in two-photon or multiphoton processes unless F(r,z) saturates lower transitions
(5) Isotopic selectivity is infinite	Molecular/assumption	Simplifies rate equation analysis but does not affect RC design concept.
(6) Time-averaged gas velocity V(r) is parallel to z axis and not z dependent	Hydrodynamic/assumption	Valid in laminar and turbulent flow for small pressure drop over RC length. Design concept still valid if V(r) also z dependent.
(7) Diffusion-related mass transfer ≪ mass transfer due to V(r)	Hydrodynamic/approximation	Basic to RC design consideration. Depletion is increasingly independent of F(r,z) distribution with increasing violation of inequality [see Sec. III.A, Eq. (7)]
(8) Gaussian optics	Optical/approximation	Good approximation for present small values of apex angle α₁.
(9) F(r,z) distribution satisfies condition for maximum depletion $\int {}_{0}^{d}F (r, z) d z \propto V (r)$	Optical/approximation	Requires approximations of Eqs. (3), (12), and (14). Typically valid to better than 10%. Depletion is not sensitive to small deviations from optimum F(r,z) if V(r) constant or slowly changing.

Abstract

Cited By

Figures (6)

Tables (3)

Equations (60)

Applied Optics